|
1
|
|
|
<?php |
|
2
|
|
|
|
|
3
|
|
|
namespace TemplesOfCode\NodesAndEdges\DFS; |
|
4
|
|
|
|
|
5
|
|
|
use InvalidArgumentException; |
|
6
|
|
|
use TemplesOfCode\NodesAndEdges\Graph; |
|
7
|
|
|
|
|
8
|
|
|
|
|
9
|
|
|
/** |
|
10
|
|
|
* Class TopologicalOrder |
|
11
|
|
|
* |
|
12
|
|
|
* Extracts topological order from a digraph |
|
13
|
|
|
* |
|
14
|
|
|
* @package TemplesOfCode\NodesAndEdges\DFS |
|
15
|
|
|
*/ |
|
16
|
|
|
class TopologicalOrder |
|
17
|
|
|
{ |
|
18
|
|
|
/** |
|
19
|
|
|
* rank[v] = rank of vertex v in order |
|
20
|
|
|
* |
|
21
|
|
|
* @var array |
|
22
|
|
|
*/ |
|
23
|
|
|
private $rank; |
|
24
|
|
|
|
|
25
|
|
|
/** |
|
26
|
|
|
* @var array |
|
27
|
|
|
*/ |
|
28
|
|
|
protected $order; |
|
29
|
|
|
|
|
30
|
|
|
/** |
|
31
|
|
|
* @var Graph |
|
32
|
|
|
*/ |
|
33
|
|
|
protected $graph; |
|
34
|
|
|
|
|
35
|
|
|
/** |
|
36
|
|
|
* TopologicalOrder constructor. |
|
37
|
|
|
* |
|
38
|
|
|
* @param Graph $g |
|
39
|
|
|
*/ |
|
40
|
|
|
public function __construct(Graph $g) |
|
41
|
|
|
{ |
|
42
|
|
|
$this->graph = $g; |
|
43
|
|
|
// delegate cycle finding to type |
|
44
|
|
|
$finder = new DirectedCycle($g); |
|
45
|
|
|
// see if any were found |
|
46
|
|
|
if ($finder->hasCycle()) { |
|
47
|
|
|
// there is at least one, we cannot continue |
|
48
|
|
|
return; |
|
49
|
|
|
} |
|
50
|
|
|
// run a dfs on g |
|
51
|
|
|
$dfs = new DepthFirstOrder($g); |
|
52
|
|
|
// get the revere order |
|
53
|
|
|
$this->order = $dfs->reversePostorder(); |
|
54
|
|
|
// init the rank list |
|
55
|
|
|
$this->rank = array_fill(0, $g->getVertices(), 0); |
|
56
|
|
|
// init |
|
57
|
|
|
$i = 0; |
|
58
|
|
|
// iterate over the |
|
59
|
|
|
foreach ($this->order as $vertex) { |
|
60
|
|
|
// set |
|
61
|
|
|
$this->rank[$vertex] = $i++; |
|
62
|
|
|
} |
|
63
|
|
|
} |
|
64
|
|
|
|
|
65
|
|
|
|
|
66
|
|
|
/** |
|
67
|
|
|
* Returns a topological order if the digraph has a topological order, |
|
68
|
|
|
* and null otherwise. |
|
69
|
|
|
* |
|
70
|
|
|
* @return array a topological order of the vertices (as an iterable) if the |
|
71
|
|
|
* digraph has a topological order (or equivalently, if the digraph is a DAG), |
|
72
|
|
|
* and null otherwise |
|
73
|
|
|
*/ |
|
74
|
|
|
public function order() |
|
75
|
|
|
{ |
|
76
|
|
|
// return list |
|
77
|
|
|
return $this->order; |
|
78
|
|
|
} |
|
79
|
|
|
|
|
80
|
|
|
/** |
|
81
|
|
|
* Does the digraph have a topological order? |
|
82
|
|
|
* |
|
83
|
|
|
* @return bool true if the digraph has a topological order (or equivalently, |
|
84
|
|
|
* if the digraph is a DAG), and false otherwise |
|
85
|
|
|
*/ |
|
86
|
|
|
public function hasOrder() |
|
87
|
|
|
{ |
|
88
|
|
|
// return check |
|
89
|
|
|
return !empty($this->order); |
|
90
|
|
|
} |
|
91
|
|
|
|
|
92
|
|
|
|
|
93
|
|
|
/** |
|
94
|
|
|
* The the rank of vertex v in the topological order; |
|
95
|
|
|
* -1 if the digraph is not a DAG |
|
96
|
|
|
* |
|
97
|
|
|
* @param int $vertex the vertex |
|
98
|
|
|
* @return int the position of $vertex in a topological order |
|
99
|
|
|
* of the digraph; -1 if the digraph is not a DAG |
|
100
|
|
|
* @throws InvalidArgumentException unless 0 <= v < V |
|
101
|
|
|
*/ |
|
102
|
|
|
public function rank(int $vertex) |
|
103
|
|
|
{ |
|
104
|
|
|
// validate |
|
105
|
|
|
Graph::validateVertex($vertex, $this->graph->getVertices()); |
|
106
|
|
|
// check for order |
|
107
|
|
|
if ($this->hasOrder()) { |
|
108
|
|
|
// return the rank |
|
109
|
|
|
return $this->rank[$vertex]; |
|
110
|
|
|
} |
|
111
|
|
|
else { |
|
112
|
|
|
// is not a DAG |
|
113
|
|
|
return -1; |
|
114
|
|
|
} |
|
115
|
|
|
} |
|
116
|
|
|
} |
templesofcode /
nodes-and-edges
